Consider the curve defined parametrically by x = t^2 + 1

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Consider the curve defined parametrically by

x = t^2 + 1, \quad y = 3t - 2, \quad t \in \mathbb R.

Answer the following. (i) Find

\dfrac{dy}{dx}

in terms of

t

. (ii) Hence determine the slope of the tangent to the curve at the point corresponding to

t = 2

. (iii) Obtain the Cartesian equation of the tangent line at this point.